The problem related to the extreme stressed state of the coal seam marginal zones is solved by the methods of loose material mechanics. Criterion for the occurrence of the limit state — simultaneous compliance with the conditions of Coulomb-Mohr on the seam and Mohr-Kuznetsov on its contact with the wall-rocks. Differential equation of the seam limit state is nonlinear and belongs to the hyperbolical type. Depending on the boundary conditions in each typical area of the seam located in the marginal zone, three boundary-value problems of the Coulomb wedge theory are consistently solved.
It is shown that the vertical component of the stress field along the longitudinal axis of the seam varies unevenly: the areas where the stresses are constant are replaced by the areas of their nonlinear increase.
The comparative estimates are given concerning the results of the stress state calculation in the marginal zone of the seam with similar results obtained using the exponential formula of changes in the given stresses, in which the exponent is represented by the total of the characteristics of the power of resistance on the seam and its contact with the rock-walls. The sizes of the seam marginal zone are established — the results of their calculation on two approaches are quite close to each other.
Solution of the elastic-plastic problem of the stress state of the massif accomodating in-seam working is greatly simplified if the diagram of the bearing pressure is set by the analytical function. In this regard, the graph of stress changes in the marginal zone is approximated by the eighth degree polynom, and its coefficients are determined by solving the system of algebraic equations, the right parts of which are the known stress values at the boundaries of the areas.